The notion that it's the Federation's job to "make sure" is the problem. They're not responsible for Nibiru; the Nibirans are. Once again, it's about respecting other cultures' right to govern themselves. It's the Nibirans' own business how they choose to interpret what they saw. Ongoing intervention on Nibiru to make sure they conformed to the Federation's idea of how they "should" develop
would be inappropriate interference. As long as it's just a single isolated incident, a freak event that doesn't repeat, then its long-term influence is likely to be minimal. Indeed, if the Nibirans are mostly organized into small bands like we see here, then there may not be much cross-contact and the image inspired by the sight of the
Enterprise might not even propagate beyond this one small community. It'll most likely just be a blip. Intervening further to try to "correct" it would just be more intrusive. It's not up to Starfleet to decide what the "correct" path for them should be in the first place. That's the whole point of the PD.
Sure, that's the simplest, most cautious path. But it shouldn't be a fanatically enforced absolute. And it shouldn't be motivated by the frankly racist belief espoused in "Homeward" that a less technologically advanced culture is too primitive to handle new ideas.
Heck, as I conveyed with the Chenari in TCO, I believe that less technologically advanced cultures often have an
easier time accepting new ideas, because so much about their world is new and unknown anyway that further discoveries are just taken in stride. Part of respecting other cultures' wisdom about their own lives is respecting their ability to cope with new information. Exposing them to that information
could have unpredictable consequences, so it's not something to be done lightly or recklessly. But it's missing the point to think it's
guaranteed to damage them. Which is why it makes more sense to approach non-interference as a general guideline, a starting default, rather than an inviolable mandate.
Actually, I've realized that TOS often fell back on the excuse of putting the
Enterprise in danger in order to force Kirk to tear down the social order despite the PD -- see "Return of the Archons," "A Taste of Armageddon," "The Apple," and "The Gamesters of Triskelion." Contrary to popular belief, Kirk wasn't specifically acting with the primary goal of changing those cultures -- he was trying to save his ship, and destroying the oppressive foundations of those cultures just happened to be the necessary way to do that. The first edition of the TNG series bible actually codifies this recurring trope, saying that the PD allows exceptions when the survival of the ship or crew is at risk (although TNG ended up going a different route later on).
Both the TOS and TNG bibles allow exceptions to the PD for vital Federation interests, which probably explains it being suspended on Organia in "Errand of Mercy." It would also apply to "The Cloud Minders," since Kirk is forced to intervene in the Stratos/Troglyte conflict by the need to get the zienite to treat the botanical plague endanering a populated planet. It's the same sort of excuse for interference as above, but with a whole planet at stake instead of just a ship.
The only real case in TOS of interference in a culture to prevent its own extinction was "For the World is Hollow...". They were certainly trying to prevent an extinction event in "The Paradise Syndrome," but barely intervened with the culture to do it, so that doesn't really count (there would've been no issue in "Pen Pals" if they'd just followed that model).
The other main reason Kirk interfered was to counter others' interference -- the Klingons in "Friday's Child" and "The Apple," or the Federation/humanity itself in "A Piece of the Action," "Bread and Circuses," "Patterns of Force," and "The Omega Glory" (wow, late season 2 was jam-packed with these).
"Spock's Brain" is a hard case to classify, and it's odd that nobody ever seems to talk about it in PD terms. Maybe it's because the Eymorgs are both primitive and hyper-advanced depending on how you look at it. And Kirk was just rescuing Spock('s brain) from their abduction, so they were the aggressors. Still, it's the one "forcibly tear down the social order" episode that doesn't have a threat to the entire
Enterprise crew to justify it.
("The Mark of Gideon" is an interesting case, in that Kirk
doesn't overthrow the Gideonite leaders or subvert their plans. He saves Odona, but then she takes his place as the disease carrier so the plan can go forward. So that's an unusual aversion of the trope of tearing down a society in the name of saving the crew.)
As I said above, it's folly to think of the Nibirans as just one culture. At their level, they're probably hundreds or thousands of small, separate bands, and a change that affects that specific community may never spread beyond it.
Again, it's folly to assume that new ideas completely replace existing ideas. Rather, they're co-opted into the belief framework that already exists, reinterpreted to fit the agendas and values the natives already have. (I actually wrote my
undergraduate history thesis paper on this topic.) If they don't fit into that existing framework, if they don't serve a purpose within it, those outside ideas will just be rejected. The only way the image of the
Enterprise would be adopted as a major theme in their culture is if it served or reinforced some cultural dynamic they already had going.
Societies are complex things. Their choices and values are shaped by a whole constellation of influences and needs, and introducing one new element isn't going to erase all those other factors. Societies choose war or peace because they see benefits in doing so, not just because some piece of paper told them to. The piece of paper is merely the justification. Look how differently our own religious texts are interpreted by factions with different agendas -- while some are inspired by the Bible or the Qur'an to pursue peace and unity and charity, others twist it into a justification for bigotry and violence and greed.
So the only way the Nibirans would throw out a belief system based on peace is if there were already a group within their society that had
its own reasons for wanting war. They'd just be using the image of the
Enterprise as an excuse for doing what they wanted to do already. So if it hadn't been that stimulus, they would've picked something else as an excuse (at least, if the volcano hadn't wiped them all out first).
Which is ridiculous. See above. Even if that one guy did toss aside the scroll in an impulsive moment, presumably they're all individuals with a range of different reactions and priorities. If enough of them have a committed belief in the principles on the scroll, then they'll refuse to abandon it, and maybe they'll punish that guy as a heretic. Belief systems tend to have built-in error correction protocols, penalties for diverging too far from their tenets. So it's not as cartoonishly easy to overthrow an entire way of life as it was implied in that scene.
Conversely, if they did discard the scroll that easily, that implies it was never as important in the first place as it appeared. Maybe it was anthropocentric to assume that the gesture of bowing toward an object represents worship at all. Or maybe it was just a convenient object of focus for their beliefs, and they substituted the
Enterprise as a better object of focus for the same beliefs, in the kind of syncretic substitution I talked about in my paper.